How to render smooth cuts at different depths
I'm not entirely sure that's what you want but maybe you could use the Boolean modifier to cut your object. You need to make your boolean object (here a cube) invisible: In Cycles Render go in the Properties panel > Object > Visibility > Ray Visibility and disable everything, and in Viewport Display choose Display as > Wire). Also pay attention to the modifiers stack order: Solidify to give your object thickness if needed, then Subdivision Surface to make it smooth (also don't forget to press W > Shade Smooth), then Boolean (Difference mode) to cut with your cube, then EdgeSplit to have sharp edges on the cut. And of course for your object try to have a nice topology with quads.